Re: Nothing in App. B of OWL Language Reference 31 March 2003

Thing and Nothing belong to two separate universes,
the universe of things which exist,
and the universe of things which do not exist.

Axioms for the universe of things which exist
    A is A
    A or not A is Thing
    A and not A is Nothing

Axioms for the universe of things which do not exist
    B is not B
    B or not B is Nothing
    B and not B is Nothing
    B is Nothing

Dick McCullough
knowledge := man do identify od existent done;
knowledge haspart proposition list;

----- Original Message ----- 
From: "Richard H. McCullough" <rhm@cdepot.net>
To: "Guus Schreiber" <schreiber@cs.vu.nl>
Cc: "webont-comments at W3C" <public-webont-comments@w3.org>
Sent: Friday, May 09, 2003 5:58 AM
Subject: Re: Nothing in App. B of OWL Language Reference 31 March 2003


>
> re: any Class, I meant some class with an extension of size > 0.
> Given any such class, ABC.
>
> <Class rdf:ID="Thing">
>    <rdfs:label>Thing</rdfs:label>
>    <unionOf rdf:parseType="Collection">
>      <Class rdf:about="#ABC"/>
>      <Class>
>        <complementOf rdf:resource="#ABC"/>
>      </Class>
>    </unionOf>
>  </Class>
>
> Strictly speaking, Nothing is the class of things that don't exist.
> I don't think it's a good idea to base your axioms on Nothing.
>
> Dick McCullough
> knowledge := man do identify od existent done;
> knowledge haspart proposition list;
>
> ----- Original Message ----- 
> From: "Guus Schreiber" <schreiber@cs.vu.nl>
> To: "Richard H. McCullough" <rhm@cdepot.net>
> Cc: "webont-comments at W3C" <public-webont-comments@w3.org>
> Sent: Friday, May 09, 2003 5:39 AM
> Subject: Re: Nothing in App. B of OWL Language Reference 31 March 2003
>
>
> > Dear Richard,
> >
> > Thanks for your comment. Responses in-line.
> >
> > Richard H. McCullough wrote:
> >
> > > Appendix B says
> > >
> > > <Class rdf:ID="Thing">
> > >   <rdfs:label>Thing</rdfs:label>
> > >   <unionOf rdf:parseType="Collection">
> > >     <Class rdf:about="#Nothing"/>
> > >     <Class>
> > >       <complementOf rdf:resource="#Nothing"/>
> > >     </Class>
> > >   </unionOf>
> > > </Class>
> > >
> > > <Class rdf:ID="Nothing">
> > >   <rdfs:label>Nothing</rdfs:label>
> > >   <complementOf rdf:resource="#Thing"/>
> > > </Class>
> > >
> > > Since the 2nd group implies that complementOf Nothing is Thing,
> > > the first group is equivalent to
> > >
> > > <Class rdf:ID="Thing">
> > >   <rdfs:label>Thing</rdfs:label>
> > >   <unionOf rdf:parseType="Collection">
> > >     <Class rdf:about="#Nothing"/>
> > >     <Class rdf about="#Thing"/>
> > >   </unionOf>
> > > </Class>
> >
> > The class axiom for owl:Thing in Appendix B of Reference defines its
> > class extension to be the extension of owl:Nothing plus its complement,
> > which means all individuals in the universe of discourse. owl:Nothing is
> > its complement, so its class extension is the empty set.
> >
> > Your revised axiom uses owl:Thing to define itself. We would prefer to
> > refrain from such recursive definitions and thus keep to the axioms as
> > they currently are.
> >
> > > which is probably what you want to say,
> > > or else omit it all together.
> > >
> > > Even better would be to replace "Nothing" with
> > > some variant of "any Class" -- which I believe
> > > is what the document says elsewhere.
> >
> > I'm not sure I understand your point. The extension of owl:Nothing is
> > the empty set, so it is not "any Class".   owl:Thing and owl:Thing
> > fulfill a special role, namely as root resp. leaf of the class lattice,
> > cf. Sec. 3.1:
> >
> > [[
> > Consequently, every OWL class is a subclass of owl:Thing and owl:Nothing
> > is a subclass of every class.
> > ]]
> >
> > Please let us know whether this response is satisfactory.
> >
> > Regards,
> > Guus Schreiber
> >
> > > ============
> > > Dick McCullough
> > > knowledge := man do identify od existent done;
> > > knowledge haspart proposition list;
> > >
> > >
> >
> > -- 
> > NOTE: new affiliation per April 1, 2003
> >
> > Free University Amsterdam, Computer Science
> > De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
> > Tel: +31 20 444 7739/7718
> > E-mail: schreiber@cs.vu.nl
> > Home page: http://www.cs.vu.nl/~guus/ [under construction]
> >
> >
>
>

Received on Friday, 23 May 2003 17:28:15 UTC